We analyze the approximation ratio of the average distance heuristic f
or the Steiner tree problem on graphs and prove nearly tight bounds fo
r the cases of complete graphs with binary weights {1, d} or weights i
n the interval [1, d], where d less than or equal to 2. The improvemen
t over other analyzed algorithms is a factor of about e approximate to
2.718, (C) 1998 John Wiley & Sons, Inc. Networks 31. 283-292, 1998.